# Definition:Statement Form

## Definition

A **statement form** is a symbolic representation of a compound statement.

It consists of statement variables along with logical connectives joining them.

It is traditional, particularly in the field of mathematical logic, to use lowercase Greek letters to stand for general formulas (the usual ones being $\phi, \psi$ and $\chi$), but more modern treatments are starting to use ordinary lowercase letters of the English alphabet, usually $p, q, r$ etc.

### Specific Form

The **specific form** of a given statement is that propositional formula from which the statement form results from replacing each distinct statement variable by a different simple statement.

## Also known as

There are various names for this concept, for example:

**statement scheme**or**schema****symbolic sentence****logical form**.

When discussing propositional logic, the terms **logical formula** or **propositional formula** are also used.

## Examples

### Napoleon

**Napoleon is dead and the world is rejoicing**

has the **statement form**

- $A \land B$

where:

- $A$ stands for
**Napoleon is dead** - $B$ stands for
**The world is rejoicing**

### Shape of Eggs

**If all eggs are not square then all eggs are round**

has the **statement form**

- $A \implies B$

where:

- $A$ stands for
**All eggs are not square** - $B$ stands for
**All eggs are round**

### Barometer

**If the barometer falls then either it will rain or it will snow**

has the **statement form**

- $A \implies \paren {B \lor C}$

where:

- $A$ stands for
**The barometer falls** - $B$ stands for
**It will rain** - $C$ stands for
**It will snow**

## Also see

- Logical Formula: A well-formed formula of a formal language used for symbolic logic.
- Propositional Formula: The logical formulae used to discuss propositional logic.

## Sources

- 1980: D.J. O'Connor and Betty Powell:
*Elementary Logic*... (previous) ... (next): $\S \text{I}: 3$: Logical Constants $(2)$ - 1988: Alan G. Hamilton:
*Logic for Mathematicians*(2nd ed.) ... (previous) ... (next): $\S 1$: Informal statement calculus: $\S 1.1$: Statements and connectives